Abelian variety isogeny class 2.113.aw_nb over $\F_{113}$

• Label: 2.113.aw_nb
• Base field: $\F_{113}$
• Dimension: $2$
• $p$-rank: $1$
• Ordinary: no
• Supersingular: no
• Simple: yes
• Geometrically simple: yes
• Primitive: yes
• Principally polarizable: yes
• Contains a Jacobian: yes

Invariants

Base field:	$\F_{113}$
Dimension:	$2$
L-polynomial:	$1 - 22 x + 339 x^{2} - 2486 x^{3} + 12769 x^{4}$
Frobenius angles:	$\pm0.274586837641$, $\pm0.374422676453$
Angle rank:	$2$ (numerical)
Number field:	4.0.6429248.1
Galois group:	$D_{4}$
Jacobians:	$84$

This isogeny class is simple and geometrically simple, primitive, not ordinary, and not supersingular. It is principally polarizable and contains a Jacobian.

Newton polygon

$p$-rank:	$1$
Slopes:	$[0, 1/2, 1/2, 1]$

Point counts

Point counts of the abelian variety

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$10601$	$165555817$	$2088117472832$	$26588439202698569$	$339454079594921197801$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$92$	$12964$	$1447166$	$163071876$	$18424207452$	$2081948399902$	$235260529660892$	$26584441989332484$	$3004041939050589662$	$339456738992358766884$

Jacobians and polarizations

This isogeny class is principally polarizable and contains the Jacobians of 84 curves (of which all are hyperelliptic):

• $y^2=24 x^6+2 x^5+77 x^4+57 x^3+16 x^2+64 x+61$
• $y^2=22 x^6+63 x^5+104 x^4+57 x^3+x^2+110 x+27$
• $y^2=19 x^6+105 x^5+54 x^4+62 x^3+110 x^2+108 x+73$
• $y^2=90 x^6+58 x^5+98 x^4+58 x^3+86 x^2+17 x+9$
• $y^2=28 x^6+14 x^5+25 x^4+34 x^3+103 x^2+28 x+7$
• $y^2=32 x^6+90 x^5+43 x^4+94 x^3+106 x^2+74 x+88$
• $y^2=74 x^6+3 x^5+103 x^4+29 x^3+78 x^2+104 x+106$
• $y^2=25 x^6+84 x^5+20 x^4+72 x^3+45 x^2+109 x+74$
• $y^2=63 x^6+68 x^5+88 x^4+68 x^3+55 x+23$
• $y^2=37 x^6+91 x^5+111 x^4+55 x^3+18 x+51$
• $y^2=x^6+101 x^5+63 x^4+102 x^3+67 x^2+75 x+75$
• $y^2=66 x^6+51 x^5+56 x^4+29 x^3+88 x^2+49 x+62$
• $y^2=81 x^6+82 x^5+51 x^4+3 x^3+60 x^2+14 x+86$
• $y^2=91 x^6+76 x^5+38 x^4+90 x^3+51 x^2+21 x+2$
• $y^2=13 x^6+73 x^5+57 x^4+52 x^3+70 x^2+47 x+43$
• $y^2=8 x^6+41 x^5+92 x^4+80 x^3+99 x^2+102 x+63$
• $y^2=84 x^6+53 x^5+91 x^4+69 x^3+84 x^2+101 x+67$
• $y^2=8 x^6+19 x^5+70 x^4+15 x^3+23 x^2+39 x+72$
• $y^2=18 x^6+4 x^5+62 x^4+88 x^3+51 x^2+20 x+59$
• $y^2=48 x^6+60 x^5+59 x^4+33 x^3+78 x^2+81 x+47$
• and

• $y^2=38 x^6+80 x^5+64 x^4+67 x^3+63 x^2+61 x+39$
• $y^2=62 x^6+84 x^5+5 x^4+32 x^3+79 x^2+41 x+33$
• $y^2=109 x^6+99 x^5+75 x^4+28 x^3+13 x^2+4 x+39$
• $y^2=90 x^6+21 x^5+66 x^4+48 x^3+93 x^2+88 x+75$
• $y^2=49 x^6+59 x^5+71 x^4+23 x^3+16 x^2+78 x+68$
• $y^2=88 x^6+110 x^5+103 x^4+36 x^3+69 x^2+33 x+37$
• $y^2=84 x^6+36 x^5+52 x^4+2 x^3+38 x^2+12 x+38$
• $y^2=42 x^6+77 x^5+12 x^4+68 x^3+46 x^2+84 x+74$
• $y^2=27 x^6+51 x^5+98 x^4+58 x^3+92 x^2+3 x+11$
• $y^2=12 x^6+64 x^5+29 x^4+83 x^3+43 x^2+34 x+24$
• $y^2=34 x^6+106 x^5+92 x^4+44 x^3+112 x^2+83 x+59$
• $y^2=102 x^6+95 x^5+46 x^4+23 x^3+63 x^2+10 x+34$
• $y^2=66 x^6+94 x^5+69 x^4+32 x^3+74 x^2+36 x+73$
• $y^2=39 x^6+23 x^5+101 x^4+105 x^3+80 x^2+27 x+38$
• $y^2=90 x^6+23 x^5+8 x^4+32 x^3+37 x^2+19 x+40$
• $y^2=65 x^6+76 x^5+25 x^4+54 x^3+73 x^2+66 x+53$
• $y^2=102 x^6+62 x^5+61 x^4+4 x^3+19 x^2+102 x+66$
• $y^2=79 x^6+107 x^5+100 x^4+13 x^3+26 x^2+13 x+27$
• $y^2=98 x^6+49 x^5+46 x^4+30 x^3+28 x^2+69 x+84$
• $y^2=97 x^6+92 x^5+44 x^4+90 x^3+23 x^2+92 x+75$
• $y^2=24 x^6+24 x^5+29 x^4+21 x^3+71 x^2+104 x+70$
• $y^2=88 x^6+27 x^5+98 x^3+65 x^2+40 x+10$
• $y^2=43 x^6+79 x^5+7 x^4+46 x^3+76 x^2+46 x+92$
• $y^2=82 x^6+31 x^5+96 x^4+101 x^3+88 x^2+38 x+11$
• $y^2=24 x^6+16 x^5+41 x^4+91 x^3+49 x^2+72$
• $y^2=51 x^6+112 x^5+20 x^4+86 x^3+50 x^2+2 x+83$
• $y^2=99 x^6+62 x^5+58 x^4+46 x^3+35 x^2+51 x+109$
• $y^2=17 x^6+12 x^4+73 x^3+47 x^2+46 x+67$
• $y^2=21 x^6+55 x^5+94 x^4+99 x^3+16 x^2+60 x+10$
• $y^2=19 x^6+39 x^5+95 x^4+53 x^3+14 x^2+46 x+31$
• $y^2=31 x^6+108 x^5+82 x^4+10 x^3+x^2+18 x+55$
• $y^2=64 x^6+62 x^5+11 x^4+58 x^3+48 x^2+79 x+57$
• $y^2=21 x^6+45 x^5+109 x^4+73 x^3+84 x^2+93 x+66$
• $y^2=58 x^6+91 x^5+87 x^4+83 x^3+9 x^2+65 x+80$
• $y^2=99 x^6+103 x^5+45 x^4+18 x^3+45 x^2+42 x+34$
• $y^2=15 x^6+82 x^5+103 x^4+106 x^3+96 x^2+70 x+34$
• $y^2=10 x^6+80 x^5+44 x^4+14 x^3+83 x^2+74 x+18$
• $y^2=108 x^6+5 x^5+112 x^4+91 x^3+82 x^2+47 x+22$
• $y^2=29 x^6+85 x^5+57 x^4+8 x^3+3 x^2+5 x+110$
• $y^2=6 x^6+84 x^5+75 x^4+51 x^3+13 x^2+105 x+60$
• $y^2=72 x^6+47 x^5+61 x^4+78 x^3+48 x^2+60 x+37$
• $y^2=76 x^6+81 x^5+53 x^4+14 x^3+92 x^2+71 x+45$
• $y^2=32 x^6+52 x^5+82 x^4+12 x^3+71 x^2+29 x+101$
• $y^2=18 x^6+50 x^5+96 x^4+50 x^3+27 x^2+58 x+65$
• $y^2=24 x^6+84 x^5+82 x^4+61 x^3+49 x^2+77 x+55$
• $y^2=94 x^6+42 x^5+86 x^4+6 x^3+97 x^2+43 x+81$
• $y^2=34 x^6+21 x^5+81 x^4+51 x^3+106 x^2+59 x+47$
• $y^2=103 x^6+92 x^5+106 x^4+112 x^3+6 x^2+106 x+33$
• $y^2=16 x^6+25 x^5+58 x^4+92 x^3+95 x^2+65 x+112$
• $y^2=46 x^6+97 x^5+90 x^4+6 x^3+64 x^2+80 x+10$
• $y^2=55 x^6+5 x^5+44 x^4+88 x^3+49 x^2+55 x+108$
• $y^2=85 x^6+56 x^5+79 x^4+10 x^3+66 x^2+25 x+36$
• $y^2=92 x^6+101 x^5+27 x^4+109 x^3+12 x^2+4 x+76$
• $y^2=65 x^6+13 x^5+96 x^4+99 x^3+103 x^2+57 x+47$
• $y^2=36 x^6+17 x^5+111 x^4+101 x^3+35 x^2+99 x+5$
• $y^2=29 x^6+71 x^5+66 x^4+8 x^3+19 x^2+64 x+83$
• $y^2=4 x^6+112 x^5+41 x^4+36 x^3+26 x^2+91 x+26$
• $y^2=14 x^6+112 x^5+24 x^3+65 x^2+102 x+59$
• $y^2=72 x^6+106 x^5+38 x^4+48 x^3+13 x^2+55 x+66$
• $y^2=89 x^6+76 x^5+54 x^4+41 x^3+8 x^2+25 x+27$
• $y^2=84 x^6+78 x^5+56 x^4+35 x^3+45 x^2+3 x+78$
• $y^2=43 x^6+23 x^5+38 x^4+7 x^3+11 x^2+39 x+24$
• $y^2=58 x^6+78 x^5+98 x^4+84 x^3+92 x^2+40 x+92$
• $y^2=110 x^6+51 x^5+64 x^4+75 x^3+28 x^2+24 x+45$

Decomposition and endomorphism algebra

All geometric endomorphisms are defined over $\F_{113}$.

Endomorphism algebra over $\F_{113}$

The endomorphism algebra of this simple isogeny class is 4.0.6429248.1.

Base change

This is a primitive isogeny class.

Twists

Below is a list of all twists of this isogeny class.

Twist	Extension degree	Common base change
2.113.w_nb	$2$	(not in LMFDB)